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PDF-22.QuadraticformsDe nition2.1(Quadraticform).LetVbeavectorspaceoverRof PDF document

2AATsothatBBTandBissymmetricThenQAQBthatisforallxy2RnwehaveQAxyQBxy4LetVbeavectorspacewithabasisEe1enandlet1n2RberealnumbersDe neQVVRasQxyPni1iyixiwherexP

2(A+AT)(sothatB=BTandBissymmetric).ThenQA=QB thatis forallx;y2RnwehaveQA(x;y)=QB(x;y).(4)LetVbeavectorspacewithabasisE=e1;:::;enandlet1;:::;n2Rberealnumbers.De neQ:VV!RasQ(x;y)=Pni=1iyixi wherex=P

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